Delta Tertiary Winding: Amp-Turn Balance Explained

[KraakeCrest]

Hi again, another question.

Please see the schematic below. It shows a wye-wye(n) with a delta tertiary winding. So this delta winding is inserted here so that we can achieve amp-turn balance with the zero sequence currents flowing on the secondary side.

I know that zero sequence currents cannot flow on the primary side due to no neutral conductor. But how does the tertiary winding help us, to let zero sequence flow on the secondary? "Current must return to the source", so below the zero sequence currents are flowing between the load and secondary and gets amp-turn balanced in the tertiary, but no zero sequence currents are returning to the source?

What am I missing here?

 

[jim hardy]

What am I missing here?

You got it.

 

[KraakeCrest]

You got it.

"Current must return to the source", I find it hard to understand that it is sufficient for the zero sequence currents to only flow from the load to secondary and get amp-turns balanced in the tertiary connection, why do they not go back to the source, i.e. primary and then back to a generator?

 

[jim hardy]

Third harmonics are in phase with one another
So on the primary wye side, write KVL around any two phases. 3rd harmonic voltage in one phase exactly cancels 3rd harmonic in the other. So no 3rd harmonic current can flow over on left side of your drawing because there's no voltage left between phases to push it. .
On secondary wye side 3rd harmonic is free to flow out the neutral.
Search on 'zero sequence currents through transformers', my google turns up several tutorials with diagrams.

If you use a spectrum analyzer to measure the current through the neutral grounding resistor of a fairly big distributed AC system that's impedance grounded, as in my power plant, you'll find a surprisingly high third harmonic content.
Then measure the phase to ground voltage's third harmonic content, you'll find it a LOT smaller.
From ratio of those you can get a rough estimate of what is the system's distributed capacitance. Z = V_3rd/I_3rd

That estimate let us answer the question "How do you know your grounding resistor is sized correctly ?"
It should be sized (per which IEEE standard I've forgotten but @Babadag probably knows ) to pass at least as much current as flows through the distributed capacitance.
Think about that for a minute - its resistance assures damping of any resonance involving distributed capacitance - search on 'ferroresonance' , which a major reason why you must ground a system.

Basics will tie all these seemingly unrelated things together. That's fun, when it 'clicks' .

 

[KraakeCrest]

Thanks, still I find it somewhat difficult to understand. Since the zero sequence currents can not flow in the primary i.e. there is no closed loop between load and source, why is the zero sequence current "allowed" to flow in the secondary in the first place if it can not get back to the source on the primary side?

 

[jim hardy]

You have to be quite literal in applying Kirchoff.

Current is charge in motion
no charge is exchanged between primary and secondary, only energy. Primary and secondary currents are in proportion because energy is conserved...

The source of all secondary current is the secondary winding.

Now, phase sequence components is not my expertise so i'll just stick with third harmonic which, if balanced, is zero sequence.
Without the tertiary winding, any secondary load that demands third harmonic current will distort the voltage wave likely 'flat-topping' it.
Tertiary (or a delta primary) gives those harmonic currents a place to amp-turn balance so the transformer can pass along energy at that frequency that's in phase in all 3 windings...

This looks like an interesting article on the subject - i only gave it a 'speed read' . But it appears to be practical..
http://www.hammondpowersolutions.com/files/HPS_article_Harmonic_Mit_FAQ.pdf
Section 11 is fascinating. Have you encountered Zig-Zag windings ?

old jim

 

[KraakeCrest]

Thanks jim, I have encountered zigzag windings and I understand its basics, but I still do not get my initial question, sorry if I am annoying and not understanding what you are saying.

Imagine the following (might not be possible in the real world, I don't know): Imagine you have a power system and the only load is some load causing zero sequence currents or third harmonics if you prefer, similar to my picture in my first post, no other currents are in the system.

From what I understand, based on this thread, there would be no current on the primary side, but the secondary currents would be present, how can current flow in the secondary if there is no current flowing in the primary? How can the transformer pass along this energy if there is no current in the primary (no current in the primary -> no energy from the source?)

Thanks.

 

[cabraham]

Triplens (harmonics that are multiples of 3) circulate in the delta tertiary, but do not appear in the wye primary. The amp-turns are not balanced, since triples are compon nets of magnetizing current. Magnetizing current is necessary to maintain core flux & is not balanced in other windings.

Without a delta tertiary, a wyw-wye come without a 3-legged E core (core type), with only 3 wires will exhibit triples in the core fluxes & line to neutral voltages. This places increased stress on the insulation & core flux.

By adding a delta tertiary, the triplens in the core flux have a closed path via the delta, & a circulating triplen current exists. But as soon as triplken current commences, a magnetic flux commences per LL, the law of Lenz. This flux opposes the original triplen flux.

FL, law of Faraday, describes relation between triplen flux & triplen voltage. Ohm's law described relation between triplen voltage, delta loop impedance, & triplen current in delta.

Each leg of the delta has an induced triplen voltage. This voltage divided by the delta impedance equals the triplen current in the delta. The impedance is resistive & inductive reactive. Even if the delta was superconductor, leakage inductance between primary & tertiary exist, resulting in a reactance. The magnetic flux due to triplen current counters the triplken core flux. The net triplen core flux gets reduced per the Lenz Law. A smaller triplen flux results in smallker triplen delta current. When steady state is reached, the core flux has very small triplen harmonic flux, due to cancellation from triplen delta current.

There is a tiny component of core triplen flux since leakage is present, coupling from primary to tertiary is imperfect. It is very small, generally negligible.

Again, magnetizing current is not amp-turn balanced. Triplens in the delta tertiary generate magnetic flux that cancels triplens in the core flux.

A similar thing happens with a wye primary & delta secondary. Triplens circulate in the delta secondary, & not in the primary.

 

[jim hardy]

Imagine you have a power system and the only load is some load causing zero sequence currents or third harmonics if you prefer, similar to my picture in my first post, no other currents are in the system.

No other currents? You mean no tertiary ?
You have postulated something that can't work. It violates Kirchoff's current law.

Here's why

Imagine three individual single phase transformers wired up as you suggest. That way there's no mixing of flux which might make a 'ghost tertiary', if you will.
Furthermore let us make their turns ratio 1::1 just for simplicity.

On primary side, each winding current must equal secondary winding current .
That defies KCL because they all three flow into the neutral.

So this transformer connection is incapable of providing only balanced zero sequence 3rd harmonic current.

What will happen is this
On primary side we have a three legged voltage divider, and neutral voltage will no longer remain stable at zero. It'll shift as required to force primary current to obey KCL, if it can.


If we back off on the requirement of only zero sequence and allow some fundamental frequency load current to also flow, 3rd can add or subtract from that and the transformer can deliver distorted load current with third harmonic content by shifting its primary side voltage division ratio . That is real and is called in the textbooks "Neutral Instability"

Of course , shifting voltage division ratio on primary side shows up as shifted voltages on secondary side too, hence the precautions against using this particular connection for a transformer. Secondary voltage becomes grossly distorted by third harmonic..

And i suspect -but do not know for sure- that what we thought was balanced zero sequence third harmonic current sprouts negative and positive sequence components. Perhaps @cabraham is better versed in that math than i.

Anyhow - my first ever attempt to figure out the mechanics of this so pardon its awkwardness. After a few more tries i should be able to arrive at the equations.
.
Here's an extract from a textbook describing neutral instability.
https://books.google.com/books?id=f...ad on wye winding neutral instability&f=false
sorry for the long link, google just does that.

It is very real. As usual, if the math says it's there it probably is. I've seen it with an oscilloscope so I'm a believer.

Here's that book

Any help ?

old jim

 

[cabraham]

The Y-Y configuration is by far the most problematic. The 3 means of mitigating its problems are as follows.
3) least desirable - a 4th wire connecting primary neutral to generator neutral. This provides a path for zero sequence currents due to unbalanced line to neutral secondary loading, as well as triplen harmonics of the magnetizing current.
But carrying 4 wires negates the advantage offered by 3 phase systems. A 3 wire system only consumes 75% the conductor weight of other numbers of phases. The towers supporting the wires would need to be bigger as well. Use of 4 wires works for short distance runs.

2) Delta tertiary - the tertiary closed path of the delta provides a path for 0 sequence & triplens. System stays balanced with 3 wires.

1) core type windings, the use of a 3 legged dual E core suppresses 0 sequence flux & triplens. The 3 legged core acts like a delta. System stays balanced in Y-Y with just 3 wires.
In a nutshell, avoid a pure Y-Y, unless a 3 legged E core pair is used. A delta tertiary is preferred for shell type & 3 single phase cores connected for 3 phase.

Wye-delta, delta-wye, delta-delta, & open delta, stay balanced & triplen harmonic free with only 3 wires.

 

[KraakeCrest]

Thanks, I will have to study this thread carefully and see if I can understand it, what is confusing me is this statement from the IEEE greenbok:

If a delta tertiary is added to a wye-wye transformer it will not be necessary to supply zero-sequence current from the primary source, since the tertiary will act as a source of zero-sequence current.

Based on that quote, and how I interpret it, primary is not needed at all if we have a tertiary delta winding for supplying zero-sequence currents. But where does the tertiary gets its energy from to act as a source?

I think the answer to my question lies in here, so I think I have to study neutral instability.

If we back off on the requirement of only zero sequence and allow some fundamental frequency load current to also flow, 3rd can add or subtract from that and the transformer can deliver distorted load current with third harmonic content by shifting its primary side voltage division ratio . That is real and is called in the textbooks "Neutral Instability"

 

[jim hardy]

But where does the tertiary gets its energy from to act as a source?

I think the answer to my question lies in here,

One never knows which little piece of the puzzle will make it 'click' for somebody else.
and as I'm not expert in phase sequence components please appreciate I'm apprehensive about mis-speaking here, ...
but this one helped me-
Conservation of energy as you are contemplating, works.
and you don't have to add energy to something to distort it, you just have to re-arrange its parts.
For your mental gyrations:
Put the primary back in that image you just posted
and contemplate that third harmonic zero sequence voltage cannot exist line to line, because what's present in one phase will be present in the other phase and by KVL those two 3rd's will cancel,,
which means the 3rd harmonic currents must originate from "something" lying downstream of your transformer's input terminals,
and there's no other energy source,

so I'm left with nonlinearities in the load (you set as a condition it draws 3rd harmonic current) and in the transformer itself.

Now the latter is well known - BH curve is nonlinear so magnetizing current required to make sinusoidal flux must contain a 3rd harmonic component
and a wye with no neutral can't accept it
so the flux and hence the voltage will distort.
Here's a brief snip from a school lab exercise that's close to the subject, he's more concise than me.
http://www.ime.pw.edu.pl/zme/dyd/mater/emitpeaa/instr_tr.pdf

That 3 wire wye primary will have neutral instability even without a load on the transformer.
But when you add a delta tertiary you have wired in series three windings that , for 3rd harmonics are in series aiding so are a short circuit.
Natural feedback - just enough current flows in the tertiary to make individual phase primary counter-emf's a nice sine wave and neutral settles down.Any help ?





..

 

[KraakeCrest]

Thanks, I think it finally "clicked" for me.

I appreciate your patience, and I will look at this closely tommorow. Now I need to rest my brain and maybe open a beer, before I take a look at it again.

Thanks!

 

[jim hardy]

I appreciate your patience, and I will look at this closely tommorow. Now I need to rest my brain and maybe open a beer, before I take a look at it again.

I got out in the yard for a while and my brain is clarifying too.

My choice of words "voltage divider" seems not ideal, and i stumbled across another site that might help me formulate a better explanation.

I am not satisfied with what I've said and will work on it tonight. Meanwhile, from this link which discusses a tangent to your question,

http://circuitglobe.com/harmonics-in-three-phase-transformers.html
He shows by algebra that third harmonic current cannot flow into a three wire wye (which he calls star).

Then he shows by algebra that the line to neutral voltages CAN contain third harmonic but without a neutral we cannot detect their presence.

5th and other non-triplens are present and detectable but we're not concerned with them...

Hmmm
so presence or absence of 3rd harmonic in line to neutral voltage cannot be detected by line to line measurement
and that means we can't tell from primary side line to line voltages whether they are present.
Even in absence of third harmonic current entering your transformer, each line to neutral voltage can contain a third harmonic.
But it won't show up in the line to line voltage. (I know I'm repeating - i do it for myself when proofreading for consistency)
It will show up as neutral displacement, because at any instant the third harmonic component adds to one (or two) of the phases and subtracts from the other(s)
and without a fourth wire the neutral is free to gyrate..

Now, adding a delta winding short circuits third harmonic component of phase voltages as i mentioned above.
Any third harmonic component of flux will induce current in those delta windings that, by Lenz's Law, opposes said third harmonic flux. That component of flux will be driven to almost zero, just as in any short circuited transformer.

>>>>It's very backward to our intuition though to think of third harmonic flux as driven not by a third harmonic component of primary current but instead by the LACK of one. <<<<

I think that's the thought key i was looking for.

Probably i should have started there, with BH curve That's what underlies the blue oops- edit - make that dark green i₀ magnetizing current's peakiness in that Warsaw University lab exercise up above

If those mostly 3rd harmonic magnetizing current peaks can't flow , the flux and voltage won't be sinewaves.
Then we get into the three phase trigonometry that hides that distortion from you when looking line to line.

if you can make a coherent presentation out of all this you'd probably do your class a big favor. When our intuition leads us to the formula we're beginning to understand, and that sure beats cramming for exams.
Run this line of thought by professor ? Maybe it'd help him figure a better way to present the subject .

I got to make use of the daylight - yard is a mess . TTFN

old jim

 

[KraakeCrest]

Thanks jim, I quote Tina Turner and say "You're simply the best".

Run this line of thought by professor ? Maybe it'd help him figure a better way to present the subject .

Good idea, I doubt I am the only one having difficulties with this one.

 

[cnh1995]

>>>It's very backward to our intuition though to think of third harmonic flux as driven not by a third harmonic component of primary current but instead by the LACK of one. <<<<

This part is discussed in this video lecture.

 

[jim hardy]

Thanks @cnh1995

i have a followup mostly typed but it rambles too much right now to offer up. Will work on it some more...

 

[jim hardy]

@cnh1995 's video - First three minutes of part 2 does with a single picture what i spent a thousand words trying to express. Nice find !
Last four minutes do a great job on Zig-Zag.

I highly recommend that video to ALL undergrad EE's . It is developed clearly and delivered logically .

I don't think i need to finish my essay , but let me sleep on it.Thanks Guys !

 

[KraakeCrest]

@jim hardy , quick follow-up questions if you don't mind? When you said:

Imagine three individual single phase transformers wired up as you suggest. That way there's no mixing of flux which might make a 'ghost tertiary', if you will.

This could be a three-limb transformer core, as shown in the picture below. And the reason for it to act as a "ghost tertiary" is because of the high reluctance path of zero sequence flux (through the transformer case e.q.), and a high reluctance path for zero sequence, results in a low impedance for zero sequence components, right?

 

[jim hardy]

This could be a three-limb transformer core, as shown in the picture below. And the reason for it to act as a "ghost tertiary" is because of the high reluctance path of zero sequence flux (through the transformer case e.q.), and a high reluctance path for zero sequence, results in a low impedance for zero sequence components, right?

I was thinking more about the transformer's operation with no tertiary.
So i added the condition to our thought experiment of 'separate transformers'
just to rule out a return path for 3rd harmonic flux
and that's what i meant by "Ghost Tertiary " ..

But yes, i think you're right.
The 3 limb can't oppose zero sequence voltage very well and that's why they caution in the IEEE test below (that Google found for me, )
when applying zero sequence voltage you must limit current to 20% of rated.
It's current that makes flux and they're keeping the iron transformer case safe with an ammeter on the exciting winding.

You've been around, haven't you ? I would learn a lot working with you. That was the fun of a maintenance career - everybody i met taught me something.
..........

For non power folks
When we just say "three phase transformer" we aren't specifying what kind of magnetics it has, "Core" or "Shell" .

The shell type has EDIT lower HIGHER zero sequence impedance because there's a return path for zero sequence flux. It's Flux that makes counter-emf and opposes flow of current
(Thanks @KraakeCrest for catching that blooper)

from http://www.electricaleasy.com/2014/04/three-phase-transformer.html

From an IEEE test standard : http://grouper.ieee.org/groups/transformers/subcommittees/performance/TF_C57_12_90/S13-C57.12.90%20section%209.5%20zero%20seq%20with%20mods.pdf

You might enjoy also https://www.scribd.com/document/57972561/Zero-Sequence-Circuit

About a ton of four five limb three phase transformers went through my metal recycle yard recently. I wanted to buy one for experimenting, at $0.30 a pound how can you go wrong? They should work well for making DC . But I decided to wait for some small enough i can pick up .
You see, I've learned my lesson. The 40 hp wound rotor motor i bought for $80 (didn't go see it before committing , just looked at pictures ) weighs 1100 pounds about 5X what i expected... had to lift it off the trailer with a friend's backhoe.old jim

 

[KraakeCrest]

Thanks jim.

The shell type has lower zero sequence impedance because there's a return path for zero sequence flux.

Hmm, should it not be: Has a higher zero sequence impedance, as there is a low reluctance path in the transformer core as impedance is proportional to 1/reluctance.

You've been around, haven't you ? I would learn a lot working with you. That was the fun of a maintenance career - everybody i met taught me something.

I have not been an active poster on pf, but I have been a member for almost a year. And I have learned a lot from other threads, and you have been a frequent contributor to many of the threads I have found very useful :)

About a ton of four limb three phase transformers went through my metal recycle yard recently.

Interesting, I wonder what the pros of using a four limb three phase transformer core would be, I will have see if google has anything interesting.

 

[jim hardy]

Hmm, should it not be: Has a higher zero sequence impedance, as there is a low reluctance path in the transformer core as impedance is proportional to 1/reluctance.

You are exactly right - my mild dyslexia at it again. Will fix the post now. THANKS !.

 

[jim hardy]

I wonder what the pros of using a four limb three phase transformer core would be,

ooops should have said shell core

They were like this, about a yard long